A block weighing 20N rests on a horizontal surface. The coefficient of static friction between the block and surface is 0.4 and the coefficient of kinetic friction is 0.20.
a. How much is the friction force exerted on the block?
b. How much will the friction force be if a horizontal force 5N is exerted on the block?
c. What is the minimum force that will start the block in motion?
d. What is the minimum force that will keep the block in motion once it has been started?
e. If the horizontal force is 10N, what is the friction force?

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Solution

a. $F_{f r i c} = μ_{s} W = 0.4 * 20 = 8 N$
b. Since $F_{a p p l i e d} < F_{f r i c}$
$F_{f r i c} = 5 N$
c. Minimum force required to start the motion $F = F_{s t a t i c f r i c} = 8 N$
d. Minimum force required to start the motion
$F = F_{k i n e t i c f r i c} = μ_{k} W = 0.2 * 20 = 4 N$
e. $F > F_{s t a t i c f r i c}$ motion started.
$F > F_{k i n e t i c f r i c}$ hence motion continues.
$F_{f r i c} = 4 N$

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a. Ffric=μsW=0.4∗20=8Nb. Since Fapplied<FfricFfric=5Nc. Minimum force required to start the motion F=Fstaticfric=8Nd. Minimum force required to start the motionF=Fkineticfric=μkW=0.2∗20=4Ne. F>Fstaticfric motion started.F>Fkineticfric hence motion continues.Ffric=4N